M. A. F. Sun dell on Galvanic Induction. 287 



7. 8. 9. 10. 11. 12. 



z . . 40 30 25 20 15 10 



J . . 5-5 12'0 19-8 34-4 69'0 154-2 



5-5 11-8 20-0 34-2 68-4 154-2 



68-4 155-4 



J (mean) T5 lH) liH) 34-3 68-6 154-6 

 In the mean the deflections in this series were :-— 

 z . . 10 15 20 25 30 40 

 J . . 154-5 68-8 34-7 19-9 11'9 5-5 

 3. .When a galvanic current of the intensity i begins in a 

 circuit, any one element ds of it induces in an element ds x of 

 another circuit an electromotive force, for the magnitude of 

 which Professor Edlund has deduced this expression : — 



+ -2(0 costf + fMcos^cos Qjtkds'ii . . (1) 



where r signifies the distance between the elements ds and ds lt 

 6 the angle between the element ds and the straight line that 

 joins the two elements, and 6 Y the angle between that line and 

 the element ds x \ a and k are constants, and h the velocity of the 

 sether* in the primary circuit. When the induction is to be 

 calculated arising from the breaking of the primary current, the 

 sign + of the expression (1) must be changed into — . The 

 amount of induction for any actual case is found by integrating 

 expression (1) for the whole length of the two circuits. In spe- 

 cial cases the result of this integration is previously known. Eor 

 example, if the circuits are plane curves in such a relative posi- 

 tion that the plane of each circuit divides the other into halves 

 situated symmetrically to the dividing plane, the whole integral 

 is equal to zero. If only the plane of one circuit divides the 

 other symmetrically, but not vice versa, the integral of the first 

 term involved in the expression (1) is zero. On the other hand, 

 the second term is of no effect if both the circuits are divided 

 symmetrically by the same plane vertical to their own planes. 

 As the above experiments concern this last case, we shall now 

 examine it a little more closely. We suppose that the circuits 

 are circles, the centres of which are on a perpendicular to their 

 planes. This perpendicular we take for ^-axis, and the plane of 

 the primary circuit for #?/-plane. Thus the origin corresponds 

 to the centre of this circuit. Every plane through the s-axis is 

 perpendicular to the circuits and divides them symmetrically. 

 Therefore the integral of the second term in the expression (1) 



* According to Professor Edlund's theory of electrical phenomena, the 

 galvanic current consists in a translative motion of the luminiferous tether 

 in the direction of the positive current. 



